Find Radius to Calculate Mass of Moon

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To calculate the mass of the Moon based on the Apollo 8 capsule's orbit, the radius must be correctly determined. The capsule orbits 112 km above the Moon's surface, which requires adding this altitude to the Moon's radius of 1.74 x 10^6 m. The correct radius for the orbit is therefore 1.74 x 10^6 m plus 112,000 m, equaling approximately 1.85 x 10^6 m. The velocity can then be calculated using the formula v = 2(pi)r/T, with T converted to seconds. Accurate unit conversions are crucial for solving the problem effectively.
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Okay, I'm having some trouble getting radius I need for the velocity that I need to solve this problem:

The manned Apollo 8 capsule was put into circular orbit 112km above the surface of the moon. The period of the orbiting space capsule was 120.5 minutes. If the radius of the moon is 1.74x10^6m, what is the mass of the moon.

Now I know how to find the mass of the moon once I get the velocity, but for some reason my velocity is coming out all wrong. I am doing v=2(pi)r/T, I know T=120.5x60= 7230seconds but I can't figure out how to find the radius. I have in my notes its 1850000m but of course I left out how I got to that and I think I have tried every combonation of numbers I have and still can't get it.

Thanks
 
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Isn't the radius of the orbit just 1.74 x 10^3 + 112 km?
 
omfg... i could have sworn those were first numbers I tried, I must have messed up somewhere on the calculator...
thanks, and sorry
 
Last edited:
Hehe :smile:. I guess you might not have converted the 112 km into metres, or the Moon's radius into km?
 
Well,Nylex,i'm surprised you haven't suggested him how to solve the problem...

Think that the gravity force (exerted by the moon on the satellite) is a centripetal force...

Daniel.
 

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